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arXiv · 0707.2863

Hermite and Gegenbauer polynomials in superspace using Clifford analysis

Hendrik De Bie·Frank Sommen
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Abstract

The Clifford-Hermite and the Clifford-Gegenbauer polynomials of standard Clifford analysis are generalized to the new framework of Clifford analysis in superspace in a merely symbolic way. This means that one does not a priori need an integration theory in superspace. Furthermore a lot of basic properties, such as orthogonality relations, differential equations and recursion formulae are proven. Finally, an interesting physical application of the super Clifford-Hermite polynomials is discussed, thus giving an interpretation to the super-dimension.

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Hendrik De Bie, Frank Sommen. 2007-07-19. Hermite and Gegenbauer polynomials in superspace using Clifford analysis. https://doi.org/10.1088/1751-8113/40/34/004

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